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Spring Topology and Dynamics Conference 2006
March 23-25, 2006
University of North Carolina at Greensboro
Greensboro, NC, USA

Organizers
Gregory Bell, Alexander Chigogidze, Paul Duvall, Jan Rychtar, Jerry Vaughan

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Non-regular Power Homogeneous Spaces
by
Nathan A. Carlson
University of Kansas

We show that the cardinality of any space with D-power homogeneous semiregularization that is either Urysohn or quasiregular is bounded by 2c(X)pc(X). This improves a result of G. J. Ridderbos who showed this bound holds for D-power homogeneous regular spaces. By introducing the notion of a local pq-base, we show that this bound can be further sharpened. We also show that no H-closed extremally disconnected space is power homogeneous. This is a variation of a result of K. Kunen who showed that no compact F-space is power homogeneous.

Date received: March 21, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cast-45.